Hi there - sounds like a great trip! My personal recommendation IF you decide to have one base would be to use Disney as a base rather than Paris as first timers, mainly because on the one occasion that I have travelled on the train back into central Paris at the end of a day at the parks, I found it to be tortuous! We had a long wait for a very crowded train and were utterly exhausted, made worse by a further metro journey within Paris when we arrived in the city. On the other hand, trains back from Paris to DLP in the evening will be much less crowded, and the train station is right next to
Disneyland Hotel so you'd be back in your room in minutes after getting off the train. I hope this makes sense!
I usually do 2 nights in Paris and 2 nights at Disney myself and this works well for me, but 1) we don't have kids and 2) we travel light as we're just there from Scotland so have a small bag each usually. The change of accommodation and transferring with lots of luggage might be more of a pain in your circumstances.
Whichever way round you decide to do it, the journey is straightforward and takes less than an hour - regular direct trains run from the DLP station (Marne La Vallee) to central Paris and it is very easy to navigate the city using the metro system, or you might fancy an open top bus to see more of the sites rather than being underground. Day trips by bus are also available organised by Disney but are obviously much more expensive and wouldn't give you as much freedom.
I also highly recommend taking the "boat bus" on the Seine when you're in Paris, it doesn't cost much as it is just a form of public transport and it is just wonderful seeing the city from the river. There's a stop at the Eiffel Tower, I love to go right along the river around sunset from Notre Dame to the tower.